by Andrew Brown
It is easy to forget that amongst his extra-curricular activities, Bernal also held a university chair in physics and was therefore responsible for a great deal of administration and some teaching. He was able to achieve this by delegating freely, for example to Stan Lenton, but above all by letting Anita Rimel run his life. From 1951, the physics department at Birkbeck was housed in a new building in Malet Street, next to the Senate House. On the entry door to Sage’s ground floor office was a sign ‘ANITA RIMEL SECRETARY’ under which the title ‘professor j.d. bernal’ appeared in much smaller letters. She was the sentinel at his gate, and in order to meet him you had to persuade her that you would not waste her professor’s precious time. He also had an emergency escape route through a backdoor that connected to the Physics Staff Room, where four of his lecturers had their desks. They became quite used to the professor beating a hasty retreat, after receiving a warning signal from Anita.14 With his own staff, Sage was generous with his time and encouragement; this extended to the student body (who came to lectures in the evenings because nearly all of them held fulltime jobs). Under Bernal, the physics department was the first to allow student representation on committees.
The atmosphere amongst the staff was generally excellent, but there was inevitably friction on occasion, most notably involving Rosalind Franklin in the completely inadequate accommodation of 21–22 Torrington Square. The most celebrated complaint came not from a staff member but from an overseas student, James Julian Ben Sammy. He had been the outstanding student at a missionary school in Trinidad and was sponsored to come to Birkbeck as a fee-paying student. He spent three years (instead of the usual two) obtaining an ordinary BSc in physics and then stayed on for another three to obtain a Special BSc. Sammy thought he deserved a first-class degree and when he did not receive one, he sued Birkbeck for breach of contract, fraud and professional negligence. The case came to trial in the High Court with Sammy appearing as the plaintiff in person. It quickly became the best farce in London and was extensively reported in The Times Law Report.15 The judge allowed him a great deal of latitude in the way he questioned witnesses from Birkbeck, but snapped when Sammy asked the Registrar if he knew the game of cricket. Sage was naturally called as a witness and was conspicuously kind to Sammy. Far from obtaining a first, it emerged that Sammy obtained a bare pass mark after Bernal had persuaded the other members of the examination board that he deserved special consideration because he was so far from home and worked hard.
During the 1950s, Bernal managed to publish four books (counting the two editions of Science in History as one book). The output from his department included 155 research papers, several of which were fundamental contributions to crystallography (on molecular biology as well as on silicates and cement). Fifteen research students gained PhD’s and 47 received MSc’s, mostly in X-ray crystallography. Apart from running his own department, Bernal was the chairman of the University of London board of studies in physics. Far from resting on his laurels, Bernal had been thinking and writing about the origin of life; in 1957 he decided to take up research into the structure of liquids again.
At first blush, the phrase ‘structure of liquids’ might seem an oxymoron, since it is their fluidity and ability to take on the shape of any container that commonly defines liquids. They have no inherent, durable structure, but at any instant the atoms in a liquid will occupy certain positions in space. Those positions, however, are continuously changing and do not form any symmetrical pattern. Bernal made his first attempt at a molecular theory of liquid structure16 in the 1930s, a few years after he and Fowler had proposed their revolutionary model of the structure of water. In his theoretical treatment, Bernal confined himself to consider the case of a liquid consisting of single, identical atoms, rather than say water, where the shape of the constituent molecules and their association by hydrogen bonds make the analysis even more complicated. It was axiomatic to Bernal that one of the main characteristics of the liquid state, its fluidity, resulted from ‘the irregularity of distribution of its component atoms or molecules and the capacity of those distributions to change under the influence of heat or the mechanical stress’. He pointed out that ‘a liquid differs fundamentally from a solid in that its configuration is not even approximately constant, but is a function of the temperature and pressure’.17 Any attempt at quantifying the irregular structure of even the simplest monatomic liquid foundered for the lack of any adequate statistical technique of three-dimensional geometry. Sage was ‘baffled by the difficulty of describing irregularity’.18
During the intervening two decades, the problem had largely been the province of mathematical physicists, who either approached the liquid state as an extension of dense gases or as an imperfect solid, resulting in theories that Sage found ‘fundamentally unsatisfying as a crystallographer, however much they might appeal to a physical chemist or a mathematician’.19 He had begun to think in much more everyday terms, for example saying that atoms in a liquid ‘have more elbow room [than in a solid] and they are not so particular about their partners’.20 What he wanted was a more graphic picture of liquid structure, as it might exist for an instant.
One approach, which was now certainly fashionable after the success of Watson and Crick, was to build models. Although Bernal had not relied heavily on model building in his previous research (unlike Lawrence Bragg, for example, going back to the 1920s), he kept a variety of models in the lab, which he regarded as a basic necessity to help thinking about problems in three dimensions.21 There had been other major breakthroughs in structural biology that seemed relevant to liquids. The α-helical structure of proteins, with its non-integral number of amino acids per turn, described by Pauling and Corey, had freed crystallographers from the mental tyranny of regular shapes. Watson and Crick’s subsequent work on the structure of spherical viruses, with their icosahedral symmetry, had taught crystallographers that although two-, three-, four- or six-fold symmetry were necessary to produce ordered, repeating structures, five-fold symmetry existed in nature even though it could not be propagated as a lattice structure. At Birkbeck, there were very talented researchers (Aaron Klug on the organic side and Alan Mackay on the inorganic) who were thinking deeply about three-dimensional geometry, and discussing their ideas with Bernal (and with Buckminster Fuller).
While all these ideas were buzzing in Bernal’s head, the actual stimulus to return to liquid structure research came during a lecture on ultra-hard alloys by Charles Frank, a professor from Bristol University. As Frank was explaining how tungsten and other metal atoms were arranged in quasi-regular shapes, including some with five-fold symmetry, Sage’s brain made the knight’s move from hard metals to liquids. Frank was a solid-state physicist, who made important observations about dislocations and other microscopic imperfections in crystals, whereas Bernal was intent on chasing down the fundamental irregularity in the structure of liquids. To help in this research, he used the services of John Mason, a Birkbeck laboratory demonstrator newly arrived from New Zealand.
One of Bernal’s first decisions was to build the type of ball-and-spoke model that was very familiar to all chemists in the context of solid crystals. Whereas X-ray scattering studies of solid crystals give information on specific atomic positions in a lattice, similar measurements of liquids give information on the distances between pairs of atoms. The statistic that describes the distribution of these pair distances is known as the radial distribution function. Spokes for the model were cut to different lengths that represented interatomic distances found in liquids, in accordance with the radial distribution function – each length of spoke was made a different colour. The model had to be free of any long-range order or pattern. Sage described his first attempt, ‘I tried to do this in the first place as casually as possible, working in my own office, being interrupted every five minutes or so and not remembering what I had done before the interruption.’22 By constructing the model, Bernal had converted one-dimensional data on the radial distribution of distances between
atoms in a liquid into three dimensions. Although there was, by design, no regularity in the model, on inspection he could find a variety of irregular shapes such as semi-octahedra and tetrahedra. Looking at the model, he drew a distinction between arranging atoms (or building blocks) in a neat pile, as was the case in crystal lattices, versus a disorganized heap, as in a liquid. For a given volume, you have fewer atoms in a heap than you do in a pile.
Bernal then asked himself the question of how the irregular polyhedra in his model fitted together. He imagined sitting on one atom and identifying all its immediate neighbours. By bisecting each spoke connecting the home atom with its neighbours, another irregular polyhedron will be formed. Mason came up with a way of creating such unusual shapes. He took a number of balls of plasticine and dusted them with chalk to stop them from sticking together. He then put the balls inside a football bladder and sucked the air out using a vacuum pump. This had the effect of pushing the soft spheres together, until they completely occupied all the remaining space. On cutting the balloon open, the plasticine spheres had squashed into ‘very beautiful and shapely polyhedra’.23 Sage was delighted to find that he was replicating an experiment carried out in 1727 by the Reverend Stephen Hales, who compressed peas in an iron pot. Hales wrote in his Vegetable Staticks that the peas ‘formed into pretty regular Dodecahedrons’.24 The plasticine was a little too soft and could be easily distorted on handling, and Mason improved the experiment by using beeswax instead and putting the spheres inside meteorological balloons that he found in Australia.25
Bernal and Mason counted the number of faces on each squashed sphere, as well as the number of sides or edges per face. The average number of faces was 13.5, and the commonest number of sides to a face was five – yet no two shapes were the same. The number of faces corresponded to the number of neighbouring atoms; in his ball-and-spoke model the average number of neighbouring atoms was 13.6. Sage was delighted when the great geometer, Donald Coxeter from Toronto University, took an interest after visiting Birkbeck. He analysed mathematically the packing of quasiequal polyhedra in space and calculated the average number of faces to be 13.56.
Sage unveiled his new models and ideas at a Friday evening discourse at the Royal Institution in October 1958. He started with what he called ‘some rather childish experiments to explain earlier and naïve views of liquid structure’, emphasizing the quality of fluidity, which earlier workers had taken as their point of departure. He told the enraptured audience that he thought this was ‘a delusive path’ and he intended to start from ‘the static and molecular structural properties of liquids’.26 His ball-and-spoke model was on view, and Mason repeated the experiment with a balloon of beeswax balls. Pointing out that no two polyhedra were identical, Bernal emphasized the predominance of five-sided faces on them.
Now you can see how very shocking such an arrangement would be to a crystallographer because it is impossible to fit these five-sided figures together in any regular way… in other words such an arrangement of points is radically different from a crystal – I could not get a regular from an irregular structure except by a very marked transition of the same nature as that between one crystalline structure and another… This explains why melting is a marked phase transition occurring at a definite temperature and with a relatively large latent heat. My analysis would show that it is impossible to pass in a continuous way from a crystalline solid to its corresponding liquid.
Only towards the end of the talk did Sage come to the actual question of fluidity. He then showed how spontaneous movement or diffusion of atoms through the liquid could result from the changes in the irregular polyhedra of neighbouring atoms. In his view, ‘it is not the fluidity of a liquid that gives rise to its irregularity. It is its irregularity that gives rise to its fluidity.’27 He concluded the talk with a mock apology to ‘the modern theoretical physicists for introducing such a simple way of looking at things, but I believe on the whole that it is better to start with a model that has some resemblance to reality’.
He did concede that to be useful, his model would need to be translated into mathematical terms. What was needed, he thought, was a new branch of mathematics called Statistical Geometry. But ‘up till now it has been very difficult to attract pure mathematicians to this and when I have tried to do so,’ he continued, ‘some of them say the problem is too difficult and others say it is too trivial’.28 He was encouraged by the start Professor Coxeter had made and hoped others would follow suit. In fact, he persuaded his eldest son, Mike, to write programs for the London University computer that generated a dense spatial model of a random distribution of points.
In 1958, Sage was elected a foreign member of the Soviet Academy of Sciences (along with his great friend Linus Pauling), nearly completing his sweep of scientific academies behind the Iron Curtain. He had already collected memberships of those in Hungary, Poland, Romania, and Bulgaria; Czechoslovakia and the German (East) Academy would soon follow. In 1959, he received the prestigious Grotius gold medal in international law (which historically is a strong form guide to the Nobel Peace Prize). By contrast, the honours accorded him in his own country were meagre, given his influence and fame. In 1962, the Royal Society did appoint him as Bakerian lecturer (a great distinction to add to his Royal Medal of 1946).
The annual Bakerian lecture, which dates back to 1775, is the Society’s premier lecture in the physical sciences. Bernal again chose for his topic ‘The structure of liquids’. He wrote to the Clerk of Birkbeck in February asking for access to the derelict 20 Torrington Square so that Mason could build him a large model in preparation for the lecture at the Royal Society.29 He explained that the model was expected to take up 2–3 cubic yards of space. When no permission was forthcoming, he gave another laboratory technician, Ian Cherry, approval to use rooms in No. 20 and told him just to drill a hole through from No. 21 to bring in an electricity cable.30 Cherry designed a special jig for the model construction, and when it was finished two or three years later, it was so big (about 4 cu. yd.) that it was entombed in a back room of No. 20 until the houses were finally demolished in 1966. For his Bakerian lecture, Bernal had to be content to show an earlier model built by Lenton and Mason. He extended his description of the modelling and mathematical work that had been going on at Birkbeck, and concluded that he and his colleagues had now substantiated the original concept of a liquid ‘being essentially a heap of molecules, that is, being homogeneous and continuous without containing hypothetical regular inner structures’.31
For the second time in his career, Sage had changed the way scientists thought about liquids. There is little doubt that the subject appealed to his sense of history. He had begun his earlier discourse at the Royal Institution with the following words.
Of all the states of matter the liquid is the least understood and yet it is the one out of which, according to the Ancients at least, all other forms of matter were made. To go no further back than Thales,* the belief that the universe was created out of water is the beginning of modern science and philosophy.32
His research returned him to the study of geometry, one of his first loves, and required him to draw on concepts that he first learned as an undergraduate at the feet of Mr Grace in Peterhouse. The realization that there was no long-range order in liquid structure was a mathematical inconvenience, but this was not a reason to reject his model. Indeed, Dorothy Wrinch’s cyclol hypothesis of protein structure, based almost entirely on mathematical neatness, failed because it could not account for the physical complexities of protein structure. The extension of X-ray crystallography first to biological substances and now to liquids called into question the whole definition of what ‘crystalline’ meant. In Bernal’s opinion, biomolecular studies had ‘broken formal crystallography, shattered it completely’.33
We clung to the rules of crystallography, constancy of angles and so forth, the limitation of symmetry notations to two-, three-, four- and six-fold, which gave us the 230 space groups, as long as we could. Brag
g hung on to them, and I’m not sure whether Perutz didn’t too, up to a point, and it needed Pauling to break them with his irrational α-helix. And so there are no rules, or the old rules are enormously changed. What we have called crystallography is a particular, small branch of crystallography, three-dimensional lattice crystallography. We are seeing now a generalized crystallography, although it hasn’t been written up as such. But I think we have many elements of many chapters of generalized crystallography in the works of Cochran, Klug, Caspar and so forth. Any kind of a repeat organization is a crystal in this general sense. Protein chains are examples of it, so is DNA, and RNA. They have their own inner logic, the same kind of logic but a different chapter of the logic that applies to the three-dimensional regular lattice crystals.
He went on to consider the structural hierarchy of biological forms, starting with the particle (‘which one might say has no dimension’), and then the fibre (one-dimension), the membrane (two-dimensions) and finally a threedimensional structure (which is not a regular crystal). He considered the issue of identity, which the biologists had first studied in the context of genetics, and proposed that biological structures were ‘combinations of arrangements of quasi-identical particles’. The key here was his favourite distinction between heaps and piles.